If you add fats and protein to white rice, it lowers the glycemic index.. I do that because I dont really like brown rice..

Correct, but two comments to make.

Firstly, remember that if you add fat and protein just to lower the GI, you are also adding calories which will effectively increase insulin requirements. So if you are choosing low GI for cutting reasons you will be defeating the purpose unless you are tracking all calories.

But secondly, I agree with what you are effectively saying. GI becomes less important as your meal is made up of progressively more protein and fat.